Analytic Solutions of a Class of Nonlinear Partial Differential Equations
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摘要: 首先,利用共轭算子的性质,将张鸿庆等提出的求伴随算子对的方法推广到了求一类非线性(即部分非线性的)算子矩阵的伴随算子向量.其次,利用机械化的构造方法给出了求解一类非线性(即,部分非线性的,且以所有线性的为其特例)非齐次微分方程组的统一理论,即通过齐次化和三角化求得恰当的变换,从而将原方程组化为较简单的形式,一般为对角化的.最后利用该方法求得了一些弹性力学方程组的解析解.Abstract: Firstly, an approach is presented for computing the adjoint operator vector of a class of nonlinear (i. e. partial-nonlinear) operator matrix by generalizing the method presented by Zhang et al. and the conjugate operators. Secondly, a united theory is given for solving a class of nonlinear (i. e. partial-nonlinear and including all linear) and non-homogeneous differential equations by the mathe-matics-mechanization method. In other words, a transformation is constructed by homogenization and triangulation which can reduce the original system to the simpler one which is diagonal. Finally, some practical applications are given in elasticity equations.
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Key words:
- AC=BD model /
- partial- nonlinear /
- adjoint /
- conjugate /
- plate and shell
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[1] 张鸿庆. 弹性力学方程组一般解的统一理论[J].大连工学院学报,1978,18(3):25-47. [2] 张鸿庆,杨光.变系数偏微分方程组一般解的构造[J].应用数学和力学, 1991,12(2):135-139. [3] ZHANG Hong-qing,MEI Jian-qin.The computational differential algebraic geometrical method of constructing the fundamental solutions of system of PDEs[A].Proceeding of the 5th UK Conference on Boundary Integral Methods[C].Liverpool: Liverpool University Press, 2005,82-89. [4] 张鸿庆.数学机械化中的AC=BD模式[J].系统科学与数学,2008,28(8):1030-1039. [5] ZHANG Hong-qing,FAN En-gui.Application of mechanical methods to partial differential equations[A].In:Wang D M,Gao X S,Eds.Mathematics Mechanization and Applications[C].London: Academic Press, 2000,409-539. [6] 张鸿庆,冯红. 非齐次线性算子方程组一般解的代数构造[J].大连理工大学学报,1994,34(3):249-255. [7] 徐芝纶.弹性力学, 第四版[M].北京:高等教育出版社, 2006. [8] 胡育佳,朱媛媛, 程昌钧.在动载荷作用下框架结构大变形分析的微分代数方法[J].应用数学与力学,2008,29(4):398-408.
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